All official letters must have a salutation and a closing statement. There are many other standard phrases that you can use inside the letter body (the reference, reason for writing, closing remarks, reference to future contact) but I'll focus on just those you asked about (opening and closing).
Salutations
If you know the person's name
Уважаемый Павел Ильич! (male)
Уважаемый господин Добровольский!
Уважаемая Татьяна Андреевна! (female)
If you don't know the person's name
Уважаемые господа,
Уважаемый/ая господин/госпожа,
Уважаемая редакция,
Closing statements
С уважением,
[Your Name]
С наилучшими пожеланиями,
[Your Name]
This is a page from this website that could answer your question.
http://masterrussian.com/aa092199.shtml
Here are the links to Russian sites that provide letter templates for official and business correspondence.
Russian business letter samples
Business correspondence samples in Russian